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Search: id:A136628
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| A136628 |
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Number of unlabeled PQ-trees with n leaves. |
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+0
2
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| 0, 1, 1, 3, 9, 29, 105, 390, 1528, 6119, 25140, 104936, 444637, 1905331, 8246619, 35988793, 158199975, 699788234, 3112679085, 13913394416, 62465305846, 281551756181, 1273583739390, 5779693081500, 26306751243309
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A PQ-tree is a rooted tree with P-type internal nodes that have at least 3 children that are reversibly ordered (the reverse of the order is equivalent to the order) and Q-type internal nodes that have at least 2 unordered children.
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 242 (3.3.91)
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LINKS
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Christian G. Bower, Table of n, a(n) for n = 0..511
Transforms in PARI
Index entries for sequences related to rooted trees
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FORMULA
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G.f. satisfies A(x) = x + (2-A(x)^2)/(2-2A(x)^2) + (1+A(x))*A(x^2)/(2-2A(x^2)) + exp(sum{i=1..inf} A(x^i)/i) - (A(x)^2+A(x^2))/2 - 2A(x) - 2
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PROGRAM
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(PARI) read("transforms_pari.txt"); {pqu(A) = A = trv_chain(A)+trv_euler(A)-trv_euler_2(A)-2*A; A[1]=0; A} {apqu(n) = local(SX, SY); SY = SX = [0, 1]; for(i=1, n, SY=concat(SY, 0); SX=concat(SX, 0); SY=SX+pqu(SY)); SY} A136628(n) = apqu(min(1, n-1))[n+1]
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CROSSREFS
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Sequence in context: A060719 A091152 A148945 this_sequence A151031 A151032 A007472
Adjacent sequences: A136625 A136626 A136627 this_sequence A136629 A136630 A136631
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jan 14 2008
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